Today Megan Bedell (Flatiron) and I called Julian Stuermer (Chicago) and Ben Montet (Chicago) to talk a bit about spectrographic measurements of radial velocity. We are looking at different extraction methods and how much information they sacrifice: Is it better to be measuring radial-velocity in the two-d image plane of the spectrograph rather than in the one-d extracted spectrum? This is not yet clear, but we have formulated the question in an information-theoretic framework.
This all relates to ancient conversations I had with Sam Roweis about spectroscopy and spectro-perfectionism (s-p). There are so many questions! In s-p, the assumption is that your spectrograph is perfectly calibrated in every way; in this case, how do you extract all the information? But the real world isn't so great, so there might be lots of experiments to do in different regimes of realism, either about the spectrograph, or about the noise, or about calibration imperfections. I promised the crew that I would figure out the Cramér–Rao bound on radial-velocity in the two-d spectrograph image and in the s-p extraction under perfect conditions.